I don't suppose that replacing the Firex with a better brand might be a quicker, easier, and cheaper solution?
UL, in its' tests, is simply death on false alarms. Even so, some brands have better reputations than others.
I'd also look at the detector placements, and the types of detectors used.
For those who don't know, here's a quick primer on detectors:
They come, most of the time, in either an "ion" or "photo-electric" type. Both must pass the same UL fire testing.
The cheapest ones out there are of the "ion" type. This type is subject to false alarms from blooms of hot air (furnace blowing on it), "burnt dust" (from the heater), and - the worst culprit - hot oil in the air (cooking).
"Photo" types cost a few dollars more, but are usually much less subject to false alarms. They can be fooled by fog (from hot water in the shower), a tiny bug getting in, and clouds of fine dust.
Detectors can also be placed to better avoid false alarms. For example, out of the path of a duct. This is much harder to do now, with the required hard-wiring.
